On non-weight representations of the N=2 superconformal algebras

In this paper, we construct a family of non-weight modules over the untwisted N = 2 superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra (modulo the center) are free of rank 2. We give a classification of isomorphism classes of such modules. Moreover, all submodules of such modules are precisely determined. In particular, those modules are not simple. The corresponding simple quotient modules are classified. Furthermore, these simple modules when restricted as modules over N = 1 superconformal algebras coincide with those modules constructed in Yang et al. (2020) [27]. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper explores the construction of non-weight modules over the untwisted N = 2 superconformal algebras, focusing on their properties over the Cartan subalgebra and the classification of isomorphism classes, as well as the determination of all submodules. The modules are not simple and the corresponding simple quotient modules are classified. Additionally, the simple modules coincide with those constructed in a previous study when restricted as modules over N = 1 superconformal algebras.